The linear system x₁ + 2x₂ − 2x₃ = 7, x₁ + x₂ + x₃ = 2, 2x₁ + 2x₂ + x₃ = 5, has the solution (1, 2,−1)^t .

a. Show that ρ(T_j) = 0.

b. Use the Jacobi method with x⁽⁰⁾ = 0 to approximate the solution to the linear system to within 10⁻⁵ in the l_∞ norm.

c. Show that ρ(T_g) = 2.

d. Show that the Gauss-Seidel method applied as in part (b) fails to give a good approximation in 25 iterations.